In a poll of 400 parents, 30% had a high income. Fifty...

In a poll of 400 parents, 30% had a high income. Fifty high-income parents oppose school vouchers. Vouchers are supported by 180 low-income parents. Hint: Create a contingency table using the data provided. (Enter your answer as a fraction or a decimal rounded to two decimal places.) What is P(oppose vouchers | high income)? (That is, what is the probability that a parent opposes vouchers, given that the parent has a high income?) P(oppose vouchers | high income) = What is P(high income | oppose vouchers)? (That is, what is the probability that a parent has a high income, given that the parent opposes vouchers?) P(high income | oppose vouchers) = What is the probability that a parent has high income or opposes vouchers? P(high income or oppose vouchers) =

Transcript

00:01 All right, so we have some questions here.

00:02 We have a 90 -frey -year -olds in the country earned more than their parents did at age 30, and in 2014, 51 % of 30 -year -olds in the same country more than their parents at age 30.

00:15 So what's the probability that it randomly selected 30 -year -old in 1970 earned more than their parents at age 30? well, 0 .93.

00:24 That's our 93%.

00:27 So randomly picked someone, 0 .93.

00:33 What's the probability that two randomly selected 30 -year -olds in 1870 earned more in their parents? so if you randomly pick 2, this is 1 .93.

00:43 If you did 2, it's 0 .93 times 0 .93 or 0 .93 squared.

00:52 And that is 0 .8649.

01:02 And let's see, what's the probability that out of 10 randomly selected 30 -olds in 1870, at least one did not earn more than his parents? okay, so 1970.

01:12 So what i did, how my brain worked, i thought about this as a binomial probability, so that distribution is given as n choose x times p to the x times one minus p to the n minus x.

01:29 Because we want, and we're x is a success, meaning they earn more than their parents.

01:34 But we want one out of 10 randomly selected.

01:37 At least one did not earn more.

01:40 At least one did not earn more.

01:41 So if x is more than their parents, x is so they earn more than their parents ' room, that means we want one minus the probability of x is 10.

01:53 Because if it's 10, that means all 10 earned more than their parents.

01:57 But we want one out of 10, or at least one out of 10, did not earn more.

02:06 So that would be 9 to 0 earned more.

02:11 No, 0 to 9, i guess, if we kind of think about, i'm a small integrator.

02:16 So we do one minus the probability the x is 10.

02:19 So i made a distribution where i took each x value.

02:24 I'm plugging this formula with the parameters.

02:26 N is 10 and p is 0 .93.

02:32 But you really could just do 1 minus this.

02:36 Let me just show you that.

02:37 The actual thing you can put 1 minus.

02:41 10 choose 10 times 0 .93 to the 10.

02:46 Times 1 minus .93 to the 10 minus 10.

02:51 And then you'd get this value .51.

02:57 Now we're going to do the same thing, but in 2014.

03:02 So i made a distribution where p was .51 in this case, and that .51 is this point is 51%.

03:13 You could also do the same thing, except replace .93 with .51.

03:21 And then out would pop this number .9988.

03:26 So the probably that one out of 10, or the out of 10 randomly selected 30 -year -olds in 2014, at least one did not earn more than their parents.

03:38 It's a very high probability that at least one did not.

03:41 So 0 .9988, and the other one, 6 -0...

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